Question

Using the given zero, find all other zeros of f(x).

-2i is a zero of f(x) = x^4 - 45x^2 - 196

Answer 1

if \(-2i\) is a zero then so is its conjugatge \(2i\) and you can factor as
\[(x-2i)(x+2i)(something)\] or
\[(x^2+4)(something)\]
find the "something" by dividing

Answer 2

\[x^4 - 45x^2 - 196=(x^2+4)(x^2-49)\] is what you get
and the zeros of \(x^2-49\) are easy to find in your head, right?

Answer 3

ohhh okay. thanks :)